A general object oriented framework for discretizing non-linear evolution equations

For a large class of non linear evolution problems we derive an abstract formulation that is based on writing the original model as a system of first order partial differential equations. Starting from this reformulation, a set of interface classes are derived that allow a problem independent implementation of various temporal and spacial discretization schemes. In particular, the abstract framework is very well suited for discretizing evolution equations with the Local Discontinuous Galerkin ansatz [1]. The implementation of the proposed framework is done within the Distributed and Unified Numerics Environment DUNE [2, 3].